A publisher sells the textbook \"Operations Management\" and its on-line learnin

Question

A publisher sells the textbook "Operations Management" and its on-line learning materials. Some students are hardworking and the other students are less-hardworking. 1/2 of all the students purchased the on-line learning materials and the others did not. If a student purchased the on-line learning materials, then the probability that this student is hard-working is 2/3. If a student did not purchase the on-line learning materials, then the probability that this student is hard-working is 1/3. If a student is randomly chosen and it is found that the student is hard-working, what is the probability that this student purchased the on-line learning materials?

Explanation / Answer

Result:

O: Online learning

H : hard working

P( O) =1/2     P( O’) = ½

P( H/O) =2/3      P( H/O’)=1/3

P(O/H) = P( H/O)* P( O)/ (P( H/O)* P( O)/+ P( H/O’)* P( O’)/)

=(2/3)*(1/2) / ((2/3)*(1/2)+ (1/3)*(1/2)

=0.66667

The required P=0.6667

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